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In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes. [ABSTRACT FROM AUTHOR]

With the continuous growth of wind power access capacity, the impact of intermittent and volatile wind power generation on the grid is becoming more and more obvious, so the research of wind power prediction has been widely concerned. The dynamic behavior of wind power time series is the external performance of complex nonlinear and multi-scale phenomena. Before choosing an appropriate prediction model, it is of great significance to analyze the characteristics of wind power time series for wind power grid system. At the same time, different sampling time scales of wind power also have an important impact on its dynamic characteristics. In this study, the chaotic dynamics behaviour of wind power time series at different time scales is discussed. The research methods include stationarity and white noise judgment, power spectral density analysis, autocorrelation function analysis, probability distribution, the Hurst index, 0–1 test algorithm for chaos, correlation dimension, maximum Lyapunov exponent, Kolmogorov entropy, recurrence plot, and information entropy method are adopted to study the chaotic dynamic behavior of wind power time series at different time scales. The actual wind power data of a wind farm at different time scales are taken as the research object for the case study. The case study results draw the following conclusions: (a) The wind power time series is non-stationary and non-white noise. (b) The direct-current and low frequency components parts store the main energy. (c) In the long-term, wind power is unpredictable. (d) The output level of wind power depends on the time scales. (e) The wind power time series obeys the fractal Brownian motion. (f) Wind power time series has chaotic characteristic. (g) Wind power time series has fractal characteristics. (h) As the time scales changes, so does the maximum prediction horizon. (i) With the decrease of time scales, the information loss rate has also declined. (j) Wind power at large time scales is more chaotic. The research results of this study have certain theoretical value and practical significance for grasping the fluctuation law of wind power and improving the prediction accuracy of wind power. [ABSTRACT FROM AUTHOR]

We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice, which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of Deng et al. [Nat. Commun. 9, 1 (2018)]. This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi–Pasta–Ulam–Tsingou lattice and a linear Klein–Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site), which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered, and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media. [ABSTRACT FROM AUTHOR]

Energy transport in one-dimensional oscillator arrays has been extensively studied to date in the conservative case, as well as under weak viscous damping. When driven at one end by a sinusoidal force, such arrays are known to exhibit the phenomenon of supratransmission, i.e. a sudden energy surge above a critical driving amplitude. In this paper, we study one-dimensional oscillator chains in the presence of hysteretic damping, and include nonlinear stiffness forces that are important for many materials at high energies. We first employ Reid's model of local hysteretic damping, and then study a new model of nearest neighbor dependent hysteretic damping to compare their supratransmission and wave packet spreading properties in a deterministic as well as stochastic setting. The results have important quantitative differences, which should be helpful when comparing the merits of the two models in specific engineering applications. [ABSTRACT FROM AUTHOR]